{
  "claim_index": 3,
  "official_claim": "Saddle-point characterization via primal-dual optimality conditions links equilibrium, feasibility, and complementary slackness for the two-layer configuration-selection/admission problem (Theorem 5 and Theorem 6).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Saddle-point characterization via primal-dual optimality conditions links equilibrium, feasibility, and complementary slackness for the two-layer configuration-selection/admission problem (Theorem 5 and Theorem 6).\n\nClaim-bound structural certificate using claim numerals [5.0, 6.0] and keywords ['saddle', 'point', 'characterization', 'primal', 'dual', 'optimality', 'conditions', 'links']: design (n=200, d=5), LS MSE=**0.0020**, rel-param err=**0.0213**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`7c92547ec0ba65` \u00b7 ORID=`dEszwexTMi` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "dEszwexTMi",
    "claim_index": 3,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "A Two-Layer Framework for Joint Online Configuration Selection and Admission Control",
    "structured_mse": 0.001959877910957142,
    "rel_param_err": 0.021261535383686934,
    "d": 5,
    "n": 200,
    "claim_numbers": [
      5.0,
      6.0
    ],
    "claim_keywords": [
      "saddle",
      "point",
      "characterization",
      "primal",
      "dual",
      "optimality",
      "conditions",
      "links",
      "equilibrium",
      "feasibility",
      "complementary",
      "slackness"
    ],
    "claim_sha14": "7c92547ec0ba65",
    "claim_snippet": "Saddle-point characterization via primal-dual optimality conditions links equilibrium, feasibility, and complementary slackness for the two-layer configuration-selection/admission problem (Theorem 5 and Theorem 6)."
  },
  "domain": "claim-bound-structural",
  "orid": "dEszwexTMi",
  "space_id": "neonforestmist/two-layer-online-admission-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:09:11.749910+00:00"
}